Econometrica: Sep, 1978, Volume 46, Issue 5

Estimation of a Distributed Lag Model under Quadratic Loss

https://doi.org/0012-9682(197809)46:5<1181:EOADLM>2.0.CO;2-D
p. 1181-1192

P. K. Trivedi

For a finite linear distribution lag model the problem of estimating the coefficients when the loss function is quadratic is considered. The explanatory variable is assumed to be generated by an autoregressive or moving average process. A result due to Szego is used to approximate the latent roots of the sample moment matrix. The approximation is then used in a comparison of the risk of four estimators--unrestricted least squares, restricted least squares, the James-Stein estimator, and the pre-test estimator. The effect of increasing autocorrelation in the explanatory variable on the relative performance of the four estimators is also studied.